To figure out whether (B) or (C) is correct, you can either plug in additional pairs of numbers or consider number properties.
No matter what numbers are selected in (B), the absolute value will be positive, so the result will be negative. (C) is only
negative if r^2 p^2 is less than 10. Therefore, (B) is the correct answer.
(D) −(1 + (−1))^2 = 0
(E) (1 + (−1))^3 = 0
J
There are variables in the question stem and in the answer choices, so this is a great time to Pick Numbers.
Say a = 2. Then 5 a + 5a + 1 = 5^2 + 5^3 = 25 + 125 = 150. Now plug a = 2 into each answer choice to see which one equals 150.
52.
(F) 62 = 36. No.
(G) 52 − 1 = 25 − 1 = 24. No.
(H) 5 2(2) + 1 = 5^4 + 1 = 625 + 1 = 626. No.
(I) (5^2 )^2 − 1 = 25^2 − 1 = 625 − 1 = 624. No.
(J) 6(5^2 ) = 6(25) = 150. Yes!
B
Number properties questions, like this one, are great candidates for Picking Numbers.
Say m = 3 and n = 5. Plug them into each answer choice.
Only (B) works. If no answer choices work with the numbers you’ve chosen, try again with different numbers.
53.
(A) 3 + 5 = 8; Not prime
(B) 3 + 5 − 1 = 7; Prime
(C) 3 + 5 − 2 = 6; Not prime
(D) 3(5) = 15; Not prime
(E) 3(5) + 1 = 16; Not prime
J
Often it is best to draw a picture to help you keep all the information straight.
X, Y, and Z are points on a line in that order.
XY = 20
54.
